Frequency changing apparatus and methods

ABSTRACT

Apparatus and methods are provided for changing the frequency of signals and in particular signals from musical instruments. In one embodiment the input signal is split into two oppositely phased signals DC restored above and below ground. The two signals are alternately passed to yield a half frequency output signal. The invention is also disclosed as it relates to frequency counting applicaTions. Also disclosed herein are various pickups for stringed instruments which may be employed with the frequency changing apparatus herein disclosed.

United States Patent [72] inventor William T- Rtsch 2,665,379 1/1954 Hadden 328/ H01 NJ]. 2,758,208 8/1956 Grayson 307/260 X hs, [21] Appl. No. 753,394 3,278,765 10/1966 Mudie 307/225 X [22} Filed Aug. 19, 1968 3,293,534 12/1966 Tillinger 307/271 X Patented Aug. 31, 1971 OTHER REFERENCES [73] Asslgnee N H Tomczak, Frequency Divider, IBM Technical Disclosure Bulletin, Vol. 6, No.4, September 1963, pp 65 & 66. 307/220 'Primary Examiner-Stanley T. Krawczewicz [54] FREQUENCY CHANGING APPARATUS AND Att0mey Louis Emnger METHODS 37 Claims, 44 Drawing Figs.

[52] US. Cl. 328/25, 84/1.01,307/220,307/260,307/27l,321/60,

328/136 ABSTRACT: Apparatus and methods are provided for chang- [51] Int. Cl H03b 19/14 ing the frequency of Signals and in particular signais from Field of Search 328/16, 25, musical instrumema In one embodiment the input signal is 30, 39, 136; 307/220, 225, 260, 271; 4/ 1 split into two oppositely phased signals DC restored above and 3321/ 69; 235/197 196 below ground. The two signals are alternately passed to yield a half frequency output signal. The invention is also disclosed as [56] M cited it relates to frequency counting applicaTionsv Also disclosed UNITED STATES PATENTS herein are various pickups for stringed instruments which may 2,349,810 5/1944 Cook 328/136 be employed with the frequency changing apparatus herein 2,399,135 4/1946 Miller et al. 328/30 X disclosed.

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\ WILLIAM T. RUSCH ATTORNEY PATENIEU was] l9?! sum 10 [1F 10 .mum nuw INVENTOR. WlLLlAM T. RUSCH A TTORNEY FREQUENCY CHANGING APPARATUS AND METHODS BACKGROUND OF THE INVENTION For a great number of years many musical instruments have been employed with electronic amplification means to provide additional volume and in some cases electronic apparatus has been employed to alter the frequency range over which the instruments normally operate; Techniques have been previously disclosed for changing, for example, dividing, the frequency of the sounds produced frommusical instruments.

When the source is of fixed known frequency (such as one note of an electronic organ) prior art frequency division has been accomplished by synchronizing a subharmonic oscillator with the source. A sinusoidal output is thereby obtained.

Alternatively, the source sinusoid has been modified into a square wave whose alternate zero crossings are used to trigger a flip-flop. The flip-flop output is, thus, at half frequency and can be made sinusoidal by tank circuit filtering.

This later method of frequency division provides a tone generation system in which output tones are derived from the normal sound of the instrument but in which such output tones may have an entirely different quality so that the known instrument may be used to generate tones sounding completely different from those characterizing the instrument.- However, assuming that the musician might like a frequency divided tone thatsounds not different from but rather as much as possible like that of the normal tone of his chosen-instrument, then the square wave flip-flop technique has major disadvantages. I

First, proper operation of this type of frequency divider demands that the original note of the instrument be stripped of most all its (distinguishing) overtones by acoustical or electrical filtering so that a relatively pure sinusoid may be fed to the square wave (clipping) circuit. Thus, even before the frequency division is begun the brilliant tone of the flute the mellow tone of the saxophone or the characteristic tone of the guitar are reduced to the dull sounding sinusoid of an audio oscillatOl.

Secondly, even if a small amount of highly attenuated (distinguishing) overtones done 't interfere with proper operation, these too are completely removed by the square wave nature of the output of the dividing flip-flop. The resulting electronic sound may indeed be different,'but it is much more aesthetically preferable to have a divided output from a guitar, for example, that still sounds like a guitar played an octave lower or, on low notes, as a bass.

Another disadvantage concerns preservation of the original amplitude envelope in the divided tone. This has been done in the past witha modulator, or with a bias control of an amplifier, or using a built-in dynamic volume control to automatically match sound level of extra octaves with the octave being played. Assuming no time constant problems (e.g., instantaneous detection of amplitude envelope so that the sharp initial zero or average level line 14. The positive going zero crossings of the squared or clipped wave (not shown) trigger the dividclarinet, etc., have waveforms considerably more complex transient of a plucked guitar string, for example, is retained in the divided output) these methods probably work. However, they, of necessity, consume extra hardware and cost to do a job which is done inherently in the halving (and doubling) techniques to be described hereinafter.

Itmay be appreciated that musical instruments do not put out pure" (i.e., sinusoidal) waveforms. It is well known that the considerable overtones or harmonics are what distinguish one instrument from another, all instruments from audio oscil lators and one musician's or one instrument's tone from anothers poor tone."

For example, many people refer to a flute as "pure and might expect its waveform to be sinusoidal. Such people have probably not heard a good flute tone with a sharp edge while watching its waveform on an oscilloscope. The complex 3 waveform is far from being sinusoidal.

The effects of even a slightlycomplex input waveform to a square wave flip-flop type divider is shown in FIG. 1. In FIG. 1A, the indentations" 12 of waveform 10 do not cross the than those shown in FIG. 1B and, unless filtering to sinusoidal shape is accomplished, render the prior art dividers useless. lndeed,-the false zero crossings cannot only render frequency division of this type impossible but may actually make the divider flip-flop run at a rate higher than the input frequency...and not necessarily by an octave.

For electric guitar applications it has been observed that the higher notes near the 12th fret of each string do tend to be reasonably sinusoidal and the prior art dividers can work without input filtering. However, the open string and 'notes at the lower frets have a complex waveform which require considerable filtering to remove false" zero crossings. A particularly obnoxious occurrence is termed the BEEP effect." When a guitar string is first struck the wave may look like wave 10 of FIG. 1A and the divider output is at half frequency as shown by the middle C in FIG. 1C. Then, possibly because of standing waves, traveling waves or body or neck structural resonances (even with solid body guitars) the waveformcan change to a type as illustrated by the wave of FIG. 1B and then quickly back to that of 1A again. The resulting short BEEP" as the divider goes from half frequency to original frequency and back to half is very annoying and objectionable. This is illustrated in FIG. 1C.

The prior art has solved this problem by capitulating to it...filtering out the valuable, pleasing and distinguishing overtones of the source note.

The loss of tonal quality caused by severe filtering of overtones is very objectionable. It results in a very electronic" sound which resembles an electronic organ perhaps more than, for example, a guitar. There have even been attempts to add overtones to get electronic instruments to sound more realistic.

Dividers for use with wind instruments use acoustical filtering provided by the instrument itself, for example by special internal microphones. The location of such a microphone is such that it receives the almost perfect sinusoidal sound necessary for the prior art dividers. The disadvantages associated with such microphones are fairly obvious. The musician either has to purchase a whole new instrument, drill a hole in his own instrument, or buy the appropriate part of an instrument which contains such a microphone. 0f more serious consequence is the very significant loss of tonal quality due to the removal of overtones. And, with such a microphone, tonal quality is sacrificed not only on the divided signal but on the straight-through signal. For example, such a microphone makes an expensive flute sound like a childs toy whistle.

In addition, to (undesirable) severe filtering, the prior art also depends on a masking" effect by which a fairly loud straight-through signal tends to mask or cover up imperfections in the divided signal.

SUMMARY OF THE INVENTION Accordingly, it is an object of this invention to provide improved frequency dividing circuits.

It is another object of this invention to provide frequency dividing circuits having amplitude preservation capability.

It is a further object of this invention to provide frequency dividing circuits which retain in the output many of the input harmonics.

It is yet another object of this invention to provide improved frequency dividing circuits for multiple input applications.

It is yet a further object of this invention to provide frequency dividing and frequency multiplying circuits.

It is still another object of this invention to provide stringed instrument pickups having electromagnetic pickup cancellation capability.

It is a further object of this invention to provide stringed instrument pickups having improved sensitivity adjustments.

It is another object of this invention to provide a novel clamping technique.

It is a further object of this invention to provide improved frequency dividing circuits for use with musical instruments.

It is yet another object of this invention to provide means for reducing the frequency of voice.

It is yet a further object of this invention to provide frequency dividing techniques not using zero crossings.

Briefly, in one embodiment, a frequency dividing technique is disclosed in which signals are generated having their peaks fixed at zero volts by DC restoration, for example. The two signals comprise the input signal after DC restoration and the inversion of that signal. The DC restored input signal is used to trigger a switch to alternately pass the DC restored signal and the inverted signal which are combined to provide a divided signal.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I A-C, a series of sketches illustrating the effects of complex input waveforms on prior art flip-flop dividers;

FIG. 2 A-D, a series of sketches illustrating the improved frequency dividing techniques herein disclosed;

FIG. 3 is a block diagram of one embodiment of a frequency divider;

FIG. 4 is a block diagram of another embodiment of a frequency divider;

FIG. 5 is a sketch illustrating another embodiment of a frequency divider;

FIG. 6 is a sketch illustrating another frequency dividing technique;

FIG. 7 is a sketch illustrating another frequency dividing technique;

FIG. 8 A-D, a series of sketches illustrating frequency dividing of relatively complex waveforms;

FIG. 9 AG, a series of sketches illustrating frequency dividing of relatively complex waveforms having double peaked characteristics;

FIG. 10 is a sketch of one embodiment of a frequency divider;

FIG. 11 is a schematic of a frequency divider circuit;

FIG. 12 is a schematic of a circuit for providing f, 2f, and f/2, and combinations thereof;

7 FIGS. 13A and 13B are sketches of guitar pickups having electromagnetic interference cancellation;

FIGS. 13C and 13D are sketches of a multipickup for guitars having isolation between pickups for preventing crosstalk;

FIGS. 14A-l4C are sketches of U-magnet pickups;

FIGS. ISA-15G are sketches of various arrangements for providing sensitivity adjustment;

FIG. 16 is a schematic of a circuit for providing f, 2f, and f/2 and combinations thereof for a multipickup guitar;

FIG. 17 is a sketch and waveforms for an improved clamping method;

FIG. I8 is a sketch illustrating a frequency divider for human voice; and

FIG. 19 is a schematic of a frequency counter.

DESCRIPTION OF PREFERRED EMBODIMENTS The techniques set forth hereinafter for dividing complex electrical signals pertain to any electrical signal, however, for illustration purposes the examples set forth relate to the complex tones of music instruments.

The basic concept of this novel frequency division will now be described in conjunction with the waveforms of FIG. 2.

The basic key to this new frequency division technique is generation of one or two signals whose peaks are fixed at zero (by addition of voltage, clamping, DC restoration, etc. Variation embodiments employing this basic idea will be discussed hereinafter.

Waveform 22 of FIG. 2A is an input signal Ecoswt. In FIG. 2B the input signal 22 is shifted so that its lower peaks just touch 0 volts, giving wave +e. A mirror image" signal e is also generated. This can be accomplished by phase inversion of the input wave 22 and shifting the inverted wave downward so that its upper peaks touch 0 volts. Or, the +e wave can itself be inverted to give e.

When the +2 signal touches 0 volts a switch signal 24 is generated. Of course, alternatively, switch signal 24 could be generated when the e signal touches zero. The switch signals trigger a flip-flop so that it is in one of its stable states from one zero touch to the next at which time it is triggered to its other stable state, as shown by waveform 26 of FIG. 2C.

The flip-flop, obviously at half frequency, controls two switches which alternately pass either +e or e to give the half frequency output 28 shown in FIG. 2D. The Fourier series for this signal is given by KE [1. cos wt/2+0.2O cos 3/2wt0.029 cos 5/2wt+...].

It may be noted from the waveform 28 and its Fourier series that the output is not perfectly sinusoidal, but is a lot closer to a sinewave than the half frequency square wave 26 (or than are the square waves generated by prior art methods).

It may also be noted that switching is done when both +2 and e are zero so that no sharp switching steps are introduced into the output waveform.

There are various ways of generating the waveforms of FIG. 2, which are the key to the new halving technique. One embodiment is illustrated in FIG. 3.

In FIG. 3, the input signal is applied to a phase splitter 30 which can comprise a single transistor stage with the signals derived from the collector and emitter thereof. The output signals from phase splitter 30 are shifted by combination with DC voltages AE-DC, and +AE-DC in summers 31 and 33 respectively to give clamped waves l-e and e. A zero sensor 32 which can be, for example, a clipping amplifier stage, a Schmitt trigger etc. delivers a switch signal pulse when signal +e touches 0 volts. Alternatively, zero sensor 32 could sense when -e touches 0 volts. The output from zero sensor 32 triggers a flip-flop 34 opening alternately on successions of triggers, switches 36 and 38, thus, alternately passing the +e and e signals to a summer 35. The half frequency output signal from summer 35 is KE [1 cos wt/2-l-0.2 cos 3/2wt0.029 cos 5/2wt+...].

In FIG. 4, e is generated not by a DC shift but rather by direct coupled inversion of the (already) generated +e waveform. The input signal is applied to a summer 40 where a DC voltage +E is added thereto to provide signal +e. Signal +e is phase inverted in a phase inverter 42 to provide the e signal. The +e signal is zero sensed to trigger flip-flop 34 and control switches 36 and 38 in the samemanner as described with respect to the embodiment of FIG. 3.

FIG. 5 is yet another embodiment of a frequency halver. In this embodiment the +AE cos wt+DC output of phase splitter 30 can be DC restored by DC voltage subtraction as shown in FIG. 3 or alternatively, as illustrated, the signal is applied to a network comprising a capacitor 44, a resistor 46 and a diode 48 where the signal is DC restored to provide signal +e. The

AE cos wt+DC, signal is applied to a network comprising a capacitor 50, a resistor 52, a transistor 54 and a resistor 56 where capacitor 50, resistor 52 and the diode input of transistor 54 provide DC restoration and the output taken at the collector of transistor 54 provides the zero sensing signals to switch flip-flop 34. The negative switch signal pulses 57 going to ground occur when e touches 0 volts (actually when it goes slightly positive since perfect DC restoration actually does not take place).

A slight variation which eliminates one switch is shown in FIG. 6. A resistor 58 having twice the value of resistors 60 and 62 combined attenuates the -Ae signal twice as much as resistors 60 and 62' attenuate the +Ae signal. Thus, when transistor 64 is open, the output =+2ee=+e. When transistor 64 is shorted, the output =e=*e. Thus, the output wave is identical to that of FIG. 2 even though only one switch is used.

Another very practical variation is illustrated in FIG. 7. Only one switch and only one clamped signal are required to give a half frequency output signal identical to that of FIG. 2.

This is made possible as follows:

The switched signal e consists of a train of pulses of the form E( 1+ cos wt). Noting that (1+ cos wt )=2 cos w/2t by trigonometric identity, it follows that e, consists of a train of cosine squared pulses. The Fourier series for e, is e,=DC 1. cos wt/2-l-O.59 cos wt-l-O.2 cos 3/2wt0.029 cos 5/2wt.+...].

This series is identical to that of the output signal series of FIG. 2 except for the 0.59 cos wt term in e, It follows that e, can be made identical to the FIG. 2 series by cancellation of 0.59 cos wt.

This is accomplished, as shown in FIG. 7. This subtraction method is advantageous for reasons mentioned and because its source (-AE cos wt) impedance can be considerably higher than that required by DC restorers. The +AE cos wt signal is applied to a DC restorer and switch signal generator 67 similar to that of FIG. 5. The +e output is then applied to a single switch arrangement as in FIG. 6. The AE cos wt signal is applied to a resistor 69 to cancel out the 0.59 cos wt term.

Several of the embodiments already shown are obviously employable for use with sources of nonconstant amplitude as well as sources of constant-amplitude.

For example, in the embodiment of FIG. 5, the amplitude of the e signal is perforce identical to that of the input signal (except for a constant gain factor which may be necessary to raise weak signals to the several volts required for good DC restoration). Similarly in FIG. 5, if the diode restorer is employed to achieve the restored +e signal, +e follows amplitude variations of the input exactly.

In the same manner the +Ae and Ae of FIG. 6 track input amplitude exactly if obtained through DC restoration. Similarly, the two vital signals of FIG. 7 (e, and the cancelling O.59 cos wt) track input amplitude exactly.

Thus, this new technique provides for exact and inherent amplitude tracking between half frequency output and input signal.

Due to the manner in which the output signal is made from the input signal, the amplitude tracking is perfect on a cycle by cycle basis. There are no time constants nor nonlinearities involved as may be the case with prior art methods. Additionally the extra hardware needed in prior art methods for amplitude tracking is eliminated by the new technique...a considerably saving in a multicircuit applications such as dividers for a six string guitar.

This inherent, instantaneous, exact and perfect amplitude tracking is another feature of the new circuit which attempts to retain as many as possible distinguishing characteristics of the input signal in the half frequency output. The key to this, of course, is the DC restoration process. The previously described frequency halving techniques have been described as used with sinusoidal sources. However, some of these embodiments can be employed with complex input signals,

In FIG. 8A there is illustrated a complex waveform 70 having a fundamental frequency as indicated by the dashed line 72 and having indentations" 74 which are caused by overtones or harmonics. Whereas this waveform is significantly different from the well filtered waveforms necessary for prior art dividers, it by no means exaggerates the complexity of the authentic" (before acoustical or electrical filtering) tones of, for example, windinstruments or electric guitars.

Obviously, a waveform such as illustrated in FIG. 8A would wreak havoc with prior art dividers which depend on the zero crossings of the squared" wave to flip their dividing flipflop.

But, in examining operation of the new divider technique it is found that the switch signal provided by the restorer/switch signal generator, transistor 54 of FIG. 5, occurs only once during each cycle of the input wave (when e of FIG. 8B touches zero..;actually when it goes slightly positive turning transistor 54 on).

Thus, output from flip-flop 34 of FIG. 5 is indeed at half frequency. Therefore, there is already a significant improvement over the prior art techniques. For, if one is content with a square wave half frequency signal, the flip-flopoutput gives reliable operation with much more input waveform complexity (less filtering) than prior art methods which not only cease dividing but may actually erroneously multiply frequency (and not necessarily by an octave) when confronted by extra fal' se zero crossings caused by overtones.

However, not settling for a square wave output, for good tonal characteristics the switched +e and -e restored waves of FIG. 8B are combined, as described previously, to achieve the half frequency output of FIG. 8D. (Obviously, either of the one-switch methods described previously can also be used even with complex waves.)

Examination of the waveform FIG. 8D shows that the indentations 76 caused by overtones are retained in the output waveform. I

As described above, the disclosed technique of frequency halving is superior to the zero crossing methods of the prior art when complex input waveforms are considered. However, the solution of one remaining problem carries it considerably further ahead.

Consider the double peak waveform of FIG. 9A which can occur as a transient condition in an unfiltered plucked guitar note and as a sustained condition in an unfiltered note from a wind instrument.

Assume DC restoration to e, FIG. 9B, and switch signal generation FIG. 9C, as achieved by transistor 54 in FIG. 5. Now, if peaks p and 12 are greater than peaks p and 12 a switch signal is generated by transistor 54 only by p and p ...when -e of FIG. 9B touches zero and normal flip-flop divisron occurs.

Similarly, normal operation occurs if p and p, are greater than p, and p ...i.e., normal operation occurs if the true" peak is greater than an immediately preceding or following false peak.

Cases occasionally arise with unfiltered musical tones where immediately adjacent true and false" peaks are of identical amplitude, as shown by the equality of p, and p of FIGS. 9A and 93.

Such a condition results in improper operation of the technique of FIG. 5. The first zero touch of -e on peak p, gives a switch signal p, which slips the flip-flop of FIG. 5. Another switch pulse is not desired until peak p occurs. But, it is obvious that the false" second switch pulse at zero touch p triggers the flip-flop of FIG. 5 erroneously.

This double peak problem could obviously be eliminated if only pulses p and p were allowed to trigger the flip-flop, pulses p, and p being rejected. The solution of this problem requires one key extra flip-flop 78 (see FIG. 10). The normal switch signal pulses generated by zero touches of -e in FIG. 9B are now called Set Pulses. Phase inversion of the input signal in phase splitter 10 of FIG. 10 followed by DC restoration and switch signal generation at 82 as in FIGS. 9D and 9E results in Reset Pulses which occur at the most negative peaks 0 of the original wave of FIG. 9A.

The set pulses are fed to one side of flip-flop 78, the reset pulses to the other side. Thus, after a reset pulse occurs, only the first of the two set pulses shown as p and p can trigger flip-flop 78.

The output of flip-flop 78 is shown in FIG. 9F.

The positive going switchings of flip-flop 78 trigger flip-flop 34 whose output FIG. 96 is seen to be reliable at half frequency as desired. Thus the double peaks no longer cause any trouble. It may be noted also that double peaks" on the bottom of the waveform have no ill efiect either. Only the first of the resulting pair of reset pulses can reset flip-flop 78.

The resulting advantages associated with being able to divide an unfiltered signal or tone still rich in its original distinguishing overtones have been discussed previously and need no further elaboration.

Slight variations in the method of FIGS. 9 and 10 (such as restoring waveform 9A positively in order to generate reset pulses without inverting waveform 9A will be discussed hereinafter.

A detailed circuit for use with instruments which produce only one note at a time (e.g., flute, saxophone or guitar if only one string is struck at a time) is shown in FIG. 11. In this embodiment the circuit set forth was employed with a flute.

A small crystal microphone 84 is attached externally to a flute (not shown) in back of the mouthpiece thereof. The output from the microphone 84 is applied to a flute preamp 86. In the reduction to practice of this embodiment the microphone output varied from about 0.02 volts peak-to-peak on low C to about 0.08 volts on the higher C two octaves up (a slope of l2db. octave). A 008 microphone resonance on high G gave output of 0.5. volts. This large variation was unpleasant from an aesthetic musical standpoint due to the over emphasis of higher harmonics as well as the loudness of higher notes. Therefore, several low pass cuts were employed in the preamp to give a flat response over the flutes three octave range. That is, the higher frequencies were attenuated to provide a flat response. If a better microphone is employed the cuts may be eliminated.

The output from preamp 86 is connected to a dual output amplifier 88. Other instruments such as the louder and lower saxophone (used with the same microphone as for the flute), trumpet, guitar, etc., would be connected to amplifier 88 without coupling through preamp 86.

Circuit operation is similar to that shown in FIG. 6. The e restore signal is attenuated by a resistor'90 twice as much as the +e restored signal so the output labeled f/2 is either +e-e/2 =e/2 when the switch transistor 100 is open or e/2= -e/2 when the switch is shorted.

The f/2 signal and the straight-through f signal are connected to an output pot 92 so that the user can have them singly or in any desired combination.

Set and reset pulses and an extra flip-flop 94 (similar to flip-flop 78 of FIG. already discussed are employed as shown. Of special note are the diode coupling of set and reset pulses to flip-flop 94 by diodes 96 and 98 and the common emitter resistor 97 of flip-flop 94. Sometimes small false" set and reset pulses not going all the way to ground are generated by false peaks in the input waveform lesser in magnitude than the true" peaks. This effect is especially severe on lower notes where the RC time constant of the DC restorers is somewhat too small and tends to restore false peaks. (When covering close to three octaves for musical instruments the best" RC time constant is perforce a compromise. It cannot be small for reasons just mentioned. It cannot be made too large because then any circuit noise causes some of the peaks of higher notes to miss being restored" with subsequent loss of set and reset pulses.

If capacitor coupling of the pulses to flip-flop 94 were used, the flip-flop could be triggered erroneously by the smaller false" pulses. This problem is overcome by the diodes 96, 98 and the emitter resistor 97. The emitters of flip-flop 94 (in the embodiment shown) are about +2 volts (one side or the other always being on). Thus the set and reset pulses must be of sufficient magnitude to get below +2 volts before they can pass through the coupling diodes. In this way, smaller false" pulses are blocked.

In this embodiment, the switch transistor 100 could be removed and a diode used instead. The diode would come from transistor 103 of flip-flop 102 and connected to the junction of a pair of resistors 104, 106 pointing away from this junction. When transistor I03 was at 0 volts the +e voltage would be shorted to ground through the diode and the conducting transistor 103. When transistor I03 was at B+ volts the diode would be reverse biased and the +e signal would pass.

In the preferred embodiment, germanium transistors and a germanium diode are used in the restorers since they are superior to silicon in terms of restoring low level signals (such as at the end of a decaying guitar note).

Due to the false peak restoration problem on low frequencies and missed peak" problems due to noise at high frequencies, the resistors in the restorers should be selected to give the optimum restorer time constant for each specific class of instruments.

Another embodiment of the frequency halving technique is shown in FIG. 12. In this embodiment, the need for a dual output amplifier is eliminated by restoring above B+ to generate the set pulses. This affords larger dynamic range with a given supply voltage and a given number of amplifier transistors. The output from the preamp 86 is applied to an amplifier 108.

The output from amplifier 108 is applied to a DC restorerreset pulse generator as described above and also applied to a circuit 110 for restoring the signal above 8+ to generate the set pulses. This circuit 110 generates set pulses at the bottoms of the wave applied thereto. The resultant positive going set pulses are coupled to the same side of flip-flop 94 as the negative going reset pulses. Whereas the +2 volt thresholding action of emitter resistor 97 of flip-flop 94 does not now apply to the positive going set pulses, a resistor 112 is added in series with the set pulse coupling diode 114 to prevent smaller false set pulses from triggering flip-flop 94. g

It may be noted that in this embodiment, the half frequency signal (fl2) is obtained by the cancellation technique described with respect to FIG. 7.

The fundamental frequency f is applied to an inverter 115 and the output from the inverter is subtracted from the switched signal in a summer circuit 116.

A double frequency output is also generated by this circuit. The output from amplifier 108 is applied to a half wave rectifier 118 to give an output of 1. cos wt+0.424 cos 2wt...Cancellation of the fundamental by the +xf subtraction in a summer 120 leaves the second harmonic. As with the f/2 signal, the amplitude of the double frequency signal tracks that of the input perfectly without variable gain as needed in the prior art.

The 2f output from summer 120, the f output from inverter 115, and the f/2 output from summer 116 are applied to potentiometers 122, 124, and 126, respectively, with the output signals therefrom being combined in a summer network 129. In this manner, the 2f, f, or f/2 signals can be obtained separately or in any desired combination. The three pots permit a vast selection of tonal gradations since the relative amplitudes of f/2, f, and 2f can be set in many different combinations. The 2f signal adds a certain brightness" of tone.

Small feedback capacitors 128, in the 2f and f/2 summing stages, respectively, remove small spikes (due to the flip-flops) which are coupled by stray pickup. The capacitors do not affect the 2f or f/2 signals themselves.

The embodiments illustrated in FIGS. 11 and 12 can be used for frequency changing with an electric guitar if only one string is plucked at a time.

In a good environment, no special modification of the guitar is required. However, if the guitar is played near a fluorescent light, for example, the electromagnetic power frequency noise induced in the guitar pickup may interfere with the frequency division process, especially on the higher notes where the compromise" restorer time constant is too large. If division is desired only on the lower strings to transform a guitar into an electric bass, the noise is no problem. However, for division over the 3% octave range of the guitar, certain pickup modifications may be desirable to reduce electromagnetic pickup.

One solution is to use a double pickup guitar with its selector switch set to center position, summing the signals from the two pickups. If the pickup coils are phased properly, hum bucking" will be achieved offering a large improvement in signal to noise ratio.

Another solution employs a single pickup I31 phase wound as shown in FIG. 13A to minimize electromagnetic pickup.

The winding is wound in one direction about three of the permanent magnets 132, 134, and 136 associated with three guitar strings (not shown) and in the opposite direction about three of the permanent magnets 135, 140, and 142 associated with the other three guitar strings (not shown). The magnets 132, 134, 136, 135, 140 and 142 can be individually raised or lowered with respect to their associated strings for providing sensitivity adjustment.

This technique is also applicable to pickups employing only a single magnet whereby the winding would be wound onehalf cw and one-half ccw. For example, in FIG. 13B a single magnet pickup 190 is shown having six adjustment screws 191 (one for each string) and the coil 192 is wound as shown. If it is desirable to perform electrically modifications (frequency halving, frequency doubling, tone change, etc.) on the output from a guitar where more than one note is struck at a time then separate pickups must be employed for each string with an output from each pickup being coupled to its individual electronic circuit for performing the desired electronic modification.

This is illustrated in FIGS. 13C and 13D where a separate pickup coil 144,-144 is used for each permanent magnet 146 -146 making up individual electromagnetic transducers for each string 148 -148 With this embodiment it is possible to employ different AGC time constants on melody and base strings so as to have the melody notes for example, hang on" longer than the has notes or vice versa. With separate transducers a stereo effect can be derived by employing two or more speakers (even to the extent of having a separate speaker for each string). To prevent crosstalk between adjacent strings, magnetic shields 150 are employed. If this shielding isabsent, an interesting effect occurs on certain combinations of notes. A frequency modulation of the f/2 notes similar to a vibrato at the beat frequency between the two notes occurs. This is not unpleasant. However, with other combinations of notes, the crosstalk results in erratic operation of the f/2 circuitry. Shielding the pickups as shown solves this problem.

Various other pickups constructed according to the invention are illustrated in FIG. 14. In FIG. 14A U-magnets are employed as the individual magnets, one magnet 200.for each string 201 (only one being shown for illustration purposes). Each magnet 200 has an associated pickup coil 202. Using a U-magnet, greater magnetic coupling is achieved with the associated string.

If the U-magnets are arranged as shown in FIG. 14B crosstalk between adjacent coils will be minimized since adjacent fluxes will be repelled. In FIG. 14C the same theory is applied. However the magnets are staggered to provide additional room in which to place their associated coils 199. In the embodiments of FIGS. 14B and 14C no shielding as shown in FIG. 13C is required.

FIGS. ISA-15G show various sensitivity adjustment arrangements. In FIG. 15A a longer U-magnet 203 is fitted within a cover plate 204 and raised or lowered with respect to string 205 to make the output from that string louder or softer. In FIG. 158 a screw adjustment is provided to change sensitivity of a bar magnet. The screw 206 is made of, for example, soft iron. An iron piece 207 is placed adjacent bar magnet 208 to give improved coupling to string 209. In FIG. 15C two screws 210 are used and the coil 211 is placed about one of the screws. Adjustment of the screws 210 cause more or less magnetic coupling to the string 212.

InFIG. 15D the magnet 213 is attached to a pair of members 214 made of, for example, soft iron which members are thereto at the poles of the magnet.

In FIG. 15F the U-magnet 219 has screw portions 220 attached thereto within a coverplate. A spring 223 is situated below the magnet whereby variable magnetic coupling to string 224 is achieved by turning the screws, the whole assembly being raised or lowered thereby. In FIG. 15G variable coupling to the string 225 is achieved by turning screw 227. Alternatively, a pair of screws could be employed. Suitable sp'rings, not shown, lower the magnet as the screw or screws are withdrawn.

Of course, sensitivity could be achieved electrically by, for example using potentiometers at the amplifier inputs or elsewhere. It may be noted that electrical sensitivity adjustment cannot be provided for in conventional single coil pickups.

The individual coils can also be alternately phased for magnetic pickup reduction of a summed straight through" signal.

Using a multiple pickup as described, and six circuits similar to that of FIG. 12 gives a high performance system producing f/2, f, and 2f for a six string guitar.

This circuitry is shown in FIG. 16 with that portion lying within the dashed lines 161 being repeated six times.

The outputs from the guitar pickup coils 144,-144 are applied to a plurality of amplifiers 160. The outputs from amplifiers are summed in a summer 162 with the summed f signals fed to a potentiometer 163 where the desired amount of f signal can be obtained and summed with the desired amount of f/2 and 2f signal in a summer 164.

The outputs from amplifier 160 are also applied to a corresponding plurality of 6db. per octave filters.165, attenuating the second harmonic which may be generated by certain of the guitar strings. Occasionally, a decaying guitar note can go through a brief period of being almost perfect second harmonic. The f/2 circuitry, even though working perfectly, divides this back to only f and not f/2. The filters alleviate this problem. The output from the filters 165 are applied to the circuits for generating the flip-flop reset and set pulses as described above. The outputs from the filters 165 are also applied to doubler 118 where 2f+xf signals are generated. The 2f +xf signals are summed together with a -xf signal in a summer 166 to provide the 2f signal at potentiometer 167. The f signal outputs from filters 165 are summed and inverted in summer 168 to generate the -xf signal which is subtracted in summer 166 as described above. The f/2 signals are generated in the same manner as described in FIG. 12 and summed in a summer 169.

In some situations the f signal can be obtained at the output of flip-flop 94 and the f/2 signal at the output of flip-flop 102. The sound produced will be of constant amplitude with no decay and will sound very much like an organ. For special effects, these outputs can be combined with the other f, f/2, etc. outputs.

Another method of DC restoration or clamping is shown in FIG. 17. Input signal e, is inverted in inverter 170 to provide c and applied to a half wave peak detector 172 to give e As shown by the arrows, the peaks of (3 are identical in magnitude to the negative peaks of e,. Obviously, addition of e, and e in summer 174 gives a clamped signal e whose lower peaks are exactly at ground (not going below ground as must happen in a conventional restorer while the C is charging). Half wave rather than full wave detection is required for complex wave shapes whose positive and negative peaks may differ in magnitude. A full wave peak detector can be used instead of half wave peak detector 172 for symmetrical waveshapes.

The techniques hereinbefore described can also be used to generate an f/4 sub/sub octave (also f/8, etc.). The output of the dividing flip-flop, for example, flip-flop 34 of FIG. 10, can trigger another flip-flop making it run at 174. This flip-flop controls a switch which shorts out alternate cycles of the f/2 waveform. Techniques already discussed then give f/4 from this switched f/2 wave.

The dividing technique can be useful in fixed tone" musical systems such as electronic organs. Where amplitude envelope is of more importance, possibly in electronic pianos, the advantages of the new circuit may make it quite useful.

As shown, frequency division circuits can handle relatively complex input waveforms. However, those produced by the human voice are too much for it except on the simpler vowel sounds.

The simple addition of band-pass filters 180,480,, as shown in FIG. 18 adapts the system for use with the human voice. Each f/2 circuit 182 handles a segment of the audio spectrum and, consequently, a less complex input waveform. The circuitry is similar to that of FIG. 16. With singing, the effect produced by f and f/2 is rather pleasant For talking, the f/2 can make a womans voice sound like that of a man. Possibly useful for greater intelligibility under certain conditions, the f/2 technique also lowers transmission bandwidth by a factor of two. For voice instructions to computers, a simpler problem is presented if woman s voice is lowered to the rang of man s.

With band-pass filtering recorded or radio music can be lowered an octave.

For special effects, a tape can be played at double speed and its output divided to be at the original frequency. (For music and speed listening).

Similarly, the f/2 output can be recorded and then played back at double speed. The resulting output will be twice as fast as recorded but at the original pitch. Again, this could be used for special musical effects or for speed listening e.g., similar to speed reading but for blind people).

In certain electronic applications (e.g., FM altimeters and depth finders) it is desired to determine the fundamental frequency of a complex waveform by use of counting techniques. With waveforms such as that of FIG. 83, prior art counters based on counting zero crossings obviously yield an erroneously high count.

With the extra flip-flop scheme of FIG. 9, the output of flip-flop 78 can be counted to yield. an accurate count by which the fundamental frequency of a complex waveform can be determined much more accurately than with prior art zero crossing techniques. This is illustrated in FIG. 19. The complex input signal is applied to phase splitter 30 with an output therefrom applied to transistor 54 to generate set pulses for flip-flop 78. The other output from phase splitter 30 after DC restoration and switch signal generation results in reset pulses for flip-flop 78. The output of flip-flop 78 is applied to a digital counter 240. The positive zero crossings of the square wave output of flip-flop 78 when counted and divided by the time of the count give the frequency of any complex wave applied at the input thereto.

Thus, it is to be understood that the embodiments shown are illustrative only, and that many variations and modifications may be made without departing from the principles of the invention herein disclosed and defined by the appended claims.

vl. Apparatus for dividing the frequency of an electrical signal comprising:

means for shifting said electrical signal such that the peaks of one extremity thereof touch zero volts;

means coupled to said shifting means for generating a mirror image of said shifted signal;

means coupled to said shifting means for generating switch signals when said peaks of said shifted signal touch zero volts; and

means for coupling alternately to an output during the periods between said generated switch signals, said shifted signal and said mirror image of said shifted signal.

2. Apparatus as defined in claim 1, wherein said coupling means includes a bistable device coupled to said means for generating switch signals and being triggered thereby; and a pair of switches coupled to said bistable device, said switches alternately coupling to an output said shifted signal and said mirror image of said shifted signal.

3. Apparatus as defined in claim I, wherein said shifting means includes means for summing said electrical signal with a voltage.

4. Apparatus as defined in claim 3, wherein said means for generating a mirror image of said shifted signal includes a phase inverter coupled to said summing means.

. 5. Apparatus as defined in claim 4, wherein said means for generating switch signals includes a zero sensor coupled to said summing means.

6. Apparatus as defined in claim 5, wherein said coupling means includes a bistable device coupled to said zero sensor; a pair of switches, one coupled to each output of said bistable device; and a summer coupled to said pair of switches.

7. Apparatus for dividing the frequency of an electrical signal comprising:

means for shifting said electrical signal such that the peaks of one extremity thereof touch zero volts;

means coupled to said shifting means for generating switch signals when said peaks touch zero volts; and

a bistable device coupled to said switch signal generating means whereby the output of said bistable device is the divided signal.

8. Apparatus for dividing the frequency of an electrical signal, comprising:

a phase splitter having first and second outputs with said electrical signal being applied to an input thereto;

first means coupled to said first output of said phase splitter for summing a signal from said first output with a first voltage such that the lower peaks of said signal from said first output will touch zero volts;

second means coupled to said second output of said phase splitter for summing a signal from said second output with a second voltage such that the upper peaks of said signal from said second output will touch zero volts;

means coupled to said first summing means for sensing when the summed signal derived from said first output touches 0 volts;

a bistable device coupled to said sensing means;

a first switch coupled to said first summing means'and to a first output from said bistable device;

a second switch coupled to said second summing means and to a second output from said bistable device; and

a summer coupled to said first and second switches.

9. Apparatus for dividing the frequency of an electrical signal, comprising:

a phase splitter having first and second outputs with said electrical signal being applied as an input thereto;

first means coupled to said first output of said phase splitter for DC restoring above a voltage level a signal from said first output;

second means coupled to said second output of said phase splitter for DC restoring below said voltage level a signal from said second output;

means coupled to said second DC restoring means for generating switch signal pulses when said DC restored signal from said second output is at its peak; and

means for coupling alternately to an output during the periods between said generated switch signals, said signals from said first and second DC restoration means.

10. Apparatus as defined in claim 9, wherein said first DC restoration means includes a capacitor; a resistor coupled from said capacitor to ground; said signal from said first output being applied to said capacitor; and a diode shunting said resistor.

11. Apparatus as defined in claim 9, wherein said second DC restoration means and said switch signal generator includes a voltage source; a capacitor; a resistor coupled from said capacitor to ground, said signal from said second output being applied to said capacitor; and a transistor having first, second, and third electrodes, said first electrode being coupled to ground, said second electrode being coupled to said resistor and said capacitor, and said third electrode being coupled to said voltage source whereby a DC restored signal is derived at the junction of said capacitor and resistor and switch signals are derived at said third electrode of said transistor.

12. Apparatus as defined in claim 11, wherein said coupling means includes a bistable device coupled to said third electrode of said transistor; a pair of switches, one coupled to each output of said bistable device; and a summer coupled to said pair of switches.

13. Apparatus as defined in claim 9, wherein said coupling means includes a bistable device coupled to said switch signal generating means; first and second series coupled resistors coupled from said second DC restoration means to the output of said apparatus; a third resistor coupled from said first DC restoration means to said apparatus output; and a switch coupled from the junction of said series coupled first and second resistors to ground, said switch being operated by said bistable device, and said third resistor having an ohmic value twice that of said first and second resistors combined.

14. Apparatus for dividing the frequency of an electrical signal, comprising:

a phase splitter having first and second outputs with said electrical signal being appliedas an input thereto;

means coupled to said second output of said phase splitter for DC restoring a signal from said second output;

means coupled to said DC restoring means for generating switch signal pulses when said DC restored signal is at its peak; a

a bistable device coupled to said switch signal generator;

first and second series connected resistors coupled from said DC restoration means to the output of said apparatus;

a third resistor coupled from said first output of said phase splitter to said output of said apparatus; and

a switchcoupled from the junction of said series connected first and second resistors to ground, said switch being coupled to and operated 'by said bistable device.

15. Apparatus for dividing the frequency of an electrical signal, comprising:

a phase splitter having first and second outputs with said I electrical signal being applied as an inputthereto;

first means coupled to said first output ofsaid phase splitter for DC restoring a signal from said first output;

second means coupled vto said second output'of said phase splitter for DC restoring a signal from said second output; 16. Apparatus as defined in claim 15, wherein said means for generating switch signal pulsesduring only one peak-each cycle of said input signal. includes a'first bistable device; means coupled to said second output of said phase shifter for generating set pulses at each top peak of said input signal, said set pulses being applied to said first bistable device; means coupled to said first output of said phase shifter for generating reset pulses at each bottom peak of said input signal, said reset pulses, being applied to said first bistable device.

17. Apparatus asdefined in claim 16, wherein said second DC restoration means and said means for generating set pulses includes a voltage source; a capacitor coupled to said second output, of said phase splitter; a resistor .coupled from said capacitor to ground; and a transistor having first, second and third electrodes, said first electrode beingcoupled to ground, said secondelectrode being coupled to said resistor and said capacitor, and said third electrode being coupled to said voltage source whereby a DC restored signal is derived at the junction. of said capacitor .and resistor and set pulses are derived at said third-electrode; of said transistor.

18. Apparatus as. defined. in claim 17, wherein said means for generating reset pulseszincludesmeans coupled to said first output of said phase. splitter for inverting the output signal from said first output of said phase splitter;-means' for DC restoring said inverted signal; and meansv for generating pulses at the-peaks of said inverted signal.

19. Apparatus as defined in claim 18, wherein said coupling means includes a second bistable device coupled to said first bistable device; a pair of switches, one: coupled to each. output f said. second bistable device;and a summer coupled tosaid pair of switches.

20. Apparatusfor dividing the frequency of an electrical signaLcomprising:

a phase splitter having first and second outputs with said electricalsignal:beingapplied'asaninput thereto;

first means coupled to said first output of said phase splitter for DC restoring a signal from said first output;

' second means coupled to said second output of said phase splitter for DC restoring a signal from said second output; means coupled to said second DC restoring means for generating switch signal pulses; and

means for coupling alternately to an output during the periods between said generated switch signals said first DC restored signal with one-half said second DC restored signal and one-half said second DC restoredsignal.

21. Apparatus for dividing the frequency of an electrical signal f, comprising:

means for generating a signal f/2+kf wherein k is a constant;

means for generating a signal kf; 1

means for summing the fl2+kf and kf signals.

22. Apparatus as defined in claim 21, wherein said means for generating a signal fl2+kf includes; means for DC restoring said electrical signal and for generating switch signal pulses, a bistable device coupled to said means for generating switch signals; a switch coupled to said bistable device and being switched thereby; and means for applying said restored signal to said summing means when said switch is open.

. 23. Apparatus 'as defined in claim 22, wherein said means for generating a signal kf includes means for inverting said electricalsignal; and means for applying said inverted signal to said summing means.

24. Apparatus as defined in claim 21, wherein said means for generating a signal f/2-l-kf includes a first bistable device; means for generating set pulses; means for generating reset pulses; means for applying said set and reset pulses to said first bistable device; a secondbistable device coupled to said first bistable device; means for DC restoring said electrical signal; a switch coupled to said second bistable device and being switched thereby; and means for applying said restored signal to said summing meanswhen said switch is open.

25. Apparatus as defined in claim 24, wherein said means for generating a signal kf includes means for inverting said electrical signal; and means for applying said inverted electrical signal to said summing means.

26. Apparatus for producing a multifrequency signal from an electrical signal f, comprising:

apparatus as defined in .claim 21 for generating a divided signal;

means for generating asignal 2f; and

' means for combining the divided signal, the f signal, and the 2f signal.

27. Apparatus as defined in claim 26, wherein said means for generating a divided signal includes a first bistable device;

.means for generating set pulses, means for generating reset pulses; means for applying said set and reset pulses to said first bistable device; a second bistable device coupled to said first bistable device; means for DC restoring said electrical signal;.,a switch coupled to said second bistable device and being switched thereby; means for applying said restored signal to said summingmeans when said switch is openymeans for inverting said electrical signal; and means for applying said inverted electrical'signalto said summing means.

28. Apparatus as defined in claim 27, wherein said means for generating a signal 2f includes a half wave rectifier to which said electrical signal is applied; and means for subtracting from the output of said half wave rectifier a portion of said electrical signal.

29. A method for dividing the frequency of an electrical signal, comprising the steps of:

shifting said electrical signal such that its lower peaks touch 0 volts; generating a mirror image of said shifted signal; generating switch signals when said lower peaks of said shiftedsignal touchesO volts; and alternately passing during the periods between said generated signals said shifted signal and said mirror image of said'shifted signal. 30. A method for dividing the frequency of an electrical signal,.comprising,the steps of:

splitting the electrical signal into two signals of opposite phase;

summing one of said two signals with a first DC voltage such that the lower peaks thereof will touch volts;

summing the other of said two signals with a second DC voltage such that the upper peaks thereof will touch 0 volts;

alternately applying to an output said summed signals.

31. The method of claim 30, wherein said summed signals are alternately applied to the output at a rate equal to the frequency of said electrical signal.

32. A method for dividing the frequency of an electrical signal, comprising the steps of:

splitting the electrical signal into two signals of opposite phase;

DC restoring one of said two signals;

DC restoring the other of said two signals;

alternately applying to an output said DC restored signals.

33. The method of claim 32, wherein said DC restored signals are alternately applied to the output at a rate equal to the frequency of said electrical signal.

34. A method for dividing the frequency of an electrical signal, comprising the steps of:

splitting the electrical signal into two signals of opposite phase;

DC restoring said two signals; and

alternately applying to an output said DC restored first signal plus twice as much of said DC restored second signal and said DC restored first signal.

35. The method of claim 52, wherein said alternate signals are applied at a rate equal to the frequency of said electrical signal. p

36. A method for dividing the frequency of an electrical signal f, comprising the steps of:

splitting the electrical signal into two signals of opposite polarity; I

DC restoring one of said two signals;

generating a signal from said DC restored signal assuming the form E (1+cos wt) where w -2-rrf;

alternately applying to an output said generated signal plus the other of said two signals and the other of said two signals.

37. The method of claim 36, wherein said alternate signals are applied at a rate equal to the frequency of said electrical signal, f.

mg UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent 3. 602.824 Dated Au ust 31. 1971 Inventofls) William T. Rus ch It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

j Column 5, line 14 that portion of the equation reading DC [1." should read --DC [1.

Column 7, line 19 the number 008" should read the word --severe--.

Column 13, after line 38, the rest of Claim 15 should read --means coupled to said outputs of said phase splitter for generating switch signal pulses during only one peak each cycle of said input signal; and

f means for coupling alternately to an output during the periods between said generated switch signal, said signals from said first and second dc restoration means.

Signed and sealed this L th day of April 1972.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT GOTTSCHALK Attestlng Officer Commissioner of Patents 

1. Apparatus for dividing the frequency of an electrical signal comprising: means for shifting said electrical signal such that the peaks of one extremity thereof touch zero volts; means coupled to said shifting means for generating a mirror image of said shifted signal; means coupled to said shifting means for generating switch signals when said peaks of said shifted signal touch zero volts; and means for coupling alternately to an output during the periods between said generated switch signals, said shifted signal and said mirror image of said shifted signal.
 2. Apparatus as defined in claim 1, wherein said coupling means includes a bistable device coupled to said means for generating switch signals and being triggered thereby; and a pair of switches coupled to said bistable device, said switches alternately coupling to an output said shifted signal and said mirror image of said shifted signal.
 3. Apparatus as defined in claim 1, wherein said shifting means includes means for summing said electrical signal with a voltage.
 4. Apparatus as defined in claim 3, wherein said means for generating a mirror image of said shifted signal includes a phase inverter coupled to said summing means.
 5. Apparatus as defined in claim 4, wherein said means for generating switch signals includes a zero sensor coupled to said summing means.
 6. Apparatus as defined in claim 5, wherein said coupling means includes a bistable device coupled to said zero sensor; a pair of switches, one coupled to each output of said bistable device; and a summer coupled to said pair of switches.
 7. Apparatus for dividing the frequency of an electrical signal comprising: means for shifting said electrical signal such that the peaks of one extremity thereof touch zero volts; means coupled to said shifting means for generating switch signals when said peaks touch zero volts; and a bistable device coupled to said switch signal generating means whereby the output of said bistable device is the divided signal.
 8. Apparatus for dividing the frequency of an electrical signal, comprising: a phase splitter having first and second outputs with said electrical signal being applied to an input thereto; first means coupled to said first output of said phase splitter for summing a signal from said first output with a first voltage such that the lower peaks of said signal from said first output will touch zero volts; second means coupled to said second output of said phase splitter for summing a signal from said second output with a second voltage such that the upper peaks of said signal from said second output will touch zero volts; means coupled to said first summing means for sensing when the summed signal derived from said first output touches 0 volts; a bistable device coupled to said sensing means; a first switch coupled to said first summing means and to a first output from said bistable device; a second switch coupled to said second summing means and to a second output from said bistable device; and a summer coupled to said first and second switches.
 9. Apparatus for dividing the frequency of an electrical signal, comprising: a phase splitter having first and second outputs with said electrical signal being applied as an input thereto; first means coupled to said first output of said phase splitter for DC restoring above a voltage level a signal from said first output; second means coupled to said second output of said phase splitter for DC restoring below said voltage level a signal from said second output; means coupled to said second DC restoring means for generating switch signal pulses when said DC restored signal from said second output is at its peak; and means for coupling alternately to an output during the periods between said generated switch signals, said signals from said first and second DC restoration means.
 10. Apparatus as defined in claim 9, wherein said first DC restoration means includes a capacitor; a resistor coupled from said capacitor to ground; said signal from said first output being applied to said capacitor; and a diode shunting said resistor.
 11. Apparatus as defined in claim 9, wherein said second DC restoration means and said switch signal generator includes a voltage source; a capacitor; a resistor coupled from said capacitor to ground, said signal from said second output being applied to said capacitor; and a transistor having first, second, and third electrodes, said first electrode being coupled to ground, said second electrode being coupled to said resistor and said capacitor, and said third electrode being coupled to said voltage source whereby a DC restored signal is derived at the junction of said capacitor and resistor and switch signals are derived at said third electrode of said transistor.
 12. Apparatus as defined in claim 11, wherein said coupling means includes a bistable device coupled to said third electrode of said transistor; a pair of switches, one coupled to each output of said bistable device; and a summer coupled to said pair of switches.
 13. Apparatus as defined in claim 9, wherein said coupling means includes a bistable device coupled to said switch signal generating means; first and second series coupled resistors coupled from said second DC restoration means to the output of said apparatus; a third resistor coupled from said first DC restoration means to said apparatus output; and a switch coupled from the junction of said series coupled first and second resistors to ground, said switch being operated by said bistable device, and said third resistor having an ohmic value twice that of said first and second resistors combined.
 14. Apparatus for dividing the frequency of an electrical signal, comprising: a phase splitter having first and second outputs with said electrical signal being applied as an input thereto; means coupled to said second output of said phase splitter for DC restoring a signal from said second output; means coupled to said DC restoring means for generating switch signal pulses when said DC restored signal is at its peak; a bistable device coupled to said switch signal generator; first and second series connected resistors coupled from said DC restoration means to the output of said apparatus; a third resistor coupled from said first output of said phase splitter to said output of said apparatus; and a switch coupled from the junction of said series connected first and second resistors to ground, said switch being coupled to and operated by said bistable device.
 15. Apparatus for dividing the frequency of an electrical signal, comprising: a phase splitter having first and second outputs with said electrical signal being applied as an input thereto; first means coupled to said first output of said phase splitter for DC restoring a signal from said first output; second means coupled to said second output of said phase splitter for DC restoring a signal from said second output;
 16. Apparatus as defined in claim 15, wherein said means for generating switch signal pulses during only one peak each cycle of said input signal includes a first bistable device; means coupled to said second output of said phase shifter for generating set pulses at each top peak of said input signal, said set pulses being applied to said first bistable device; means coupled to said first output of said phase shifter for generating reset pulses at each bottom peak of said input signal, said reset pulses being applied to said first bistable device.
 17. Apparatus as defined in claim 16, wherein said second DC restoration means and said means for generating set pulses includes a voltage source; a capacitor coupled to said second output of said phase splitter; a resistor coupled from said capacitor to ground; and a transIstor having first, second and third electrodes, said first electrode being coupled to ground, said second electrode being coupled to said resistor and said capacitor, and said third electrode being coupled to said voltage source whereby a DC restored signal is derived at the junction of said capacitor and resistor and set pulses are derived at said third electrode of said transistor.
 18. Apparatus as defined in claim 17, wherein said means for generating reset pulses includes means coupled to said first output of said phase splitter for inverting the output signal from said first output of said phase splitter; means for DC restoring said inverted signal; and means for generating pulses at the peaks of said inverted signal.
 19. Apparatus as defined in claim 18, wherein said coupling means includes a second bistable device coupled to said first bistable device; a pair of switches, one coupled to each output of said second bistable device; and a summer coupled to said pair of switches.
 20. Apparatus for dividing the frequency of an electrical signal, comprising: a phase splitter having first and second outputs with said electrical signal being applied as an input thereto; first means coupled to said first output of said phase splitter for DC restoring a signal from said first output; second means coupled to said second output of said phase splitter for DC restoring a signal from said second output; means coupled to said second DC restoring means for generating switch signal pulses; and means for coupling alternately to an output during the periods between said generated switch signals said first DC restored signal with one-half said second DC restored signal and one-half said second DC restored signal.
 21. Apparatus for dividing the frequency of an electrical signal f, comprising: means for generating a signal f/2+ kf wherein k is a constant; means for generating a signal -kf; means for summing the f/2+ kf and -kf signals.
 22. Apparatus as defined in claim 21, wherein said means for generating a signal f/2+ kf includes; means for DC restoring said electrical signal and for generating switch signal pulses, a bistable device coupled to said means for generating switch signals; a switch coupled to said bistable device and being switched thereby; and means for applying said restored signal to said summing means when said switch is open.
 23. Apparatus as defined in claim 22, wherein said means for generating a signal -kf includes means for inverting said electrical signal; and means for applying said inverted signal to said summing means.
 24. Apparatus as defined in claim 21, wherein said means for generating a signal f/2+ kf includes a first bistable device; means for generating set pulses; means for generating reset pulses; means for applying said set and reset pulses to said first bistable device; a second bistable device coupled to said first bistable device; means for DC restoring said electrical signal; a switch coupled to said second bistable device and being switched thereby; and means for applying said restored signal to said summing means when said switch is open.
 25. Apparatus as defined in claim 24, wherein said means for generating a signal -kf includes means for inverting said electrical signal; and means for applying said inverted electrical signal to said summing means.
 26. Apparatus for producing a multifrequency signal from an electrical signal f, comprising: apparatus as defined in claim 21 for generating a divided signal; means for generating a signal 2f; and means for combining the divided signal, the f signal, and the 2f signal.
 27. Apparatus as defined in claim 26, wherein said means for generating a divided signal includes a first bistable device; means for generating set pulses, means foR generating reset pulses; means for applying said set and reset pulses to said first bistable device; a second bistable device coupled to said first bistable device; means for DC restoring said electrical signal; a switch coupled to said second bistable device and being switched thereby; means for applying said restored signal to said summing means when said switch is open; means for inverting said electrical signal; and means for applying said inverted electrical signal to said summing means.
 28. Apparatus as defined in claim 27, wherein said means for generating a signal 2f includes a half wave rectifier to which said electrical signal is applied; and means for subtracting from the output of said half wave rectifier a portion of said electrical signal.
 29. A method for dividing the frequency of an electrical signal, comprising the steps of: shifting said electrical signal such that its lower peaks touch 0 volts; generating a mirror image of said shifted signal; generating switch signals when said lower peaks of said shifted signal touches 0 volts; and alternately passing during the periods between said generated signals said shifted signal and said mirror image of said shifted signal.
 30. A method for dividing the frequency of an electrical signal, comprising the steps of: splitting the electrical signal into two signals of opposite phase; summing one of said two signals with a first DC voltage such that the lower peaks thereof will touch 0 volts; summing the other of said two signals with a second DC voltage such that the upper peaks thereof will touch 0 volts; alternately applying to an output said summed signals.
 31. The method of claim 30, wherein said summed signals are alternately applied to the output at a rate equal to the frequency of said electrical signal.
 32. A method for dividing the frequency of an electrical signal, comprising the steps of: splitting the electrical signal into two signals of opposite phase; DC restoring one of said two signals; DC restoring the other of said two signals; alternately applying to an output said DC restored signals.
 33. The method of claim 32, wherein said DC restored signals are alternately applied to the output at a rate equal to the frequency of said electrical signal.
 34. A method for dividing the frequency of an electrical signal, comprising the steps of: splitting the electrical signal into two signals of opposite phase; DC restoring said two signals; and alternately applying to an output said DC restored first signal plus twice as much of said DC restored second signal and said DC restored first signal.
 35. The method of claim 52, wherein said alternate signals are applied at a rate equal to the frequency of said electrical signal.
 36. A method for dividing the frequency of an electrical signal f, comprising the steps of: splitting the electrical signal into two signals of opposite polarity; DC restoring one of said two signals; generating a signal from said DC restored signal assuming the form E (1+ cos wt) where w 2 pi f; alternately applying to an output said generated signal plus the other of said two signals and the other of said two signals.
 37. The method of claim 36, wherein said alternate signals are applied at a rate equal to the frequency of said electrical signal, f. 